TSTP Solution File: LCL947_10 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL947_10 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 22 15:39:14 EDT 2023
% Result : Theorem 49.99s 32.70s
% Output : Proof 50.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL947_10 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 11:55:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 49.99/32.70 % SZS status Theorem
% 49.99/32.70 % SZS output start Proof
% 49.99/32.70 tff(tptp_fun___ki_accessible__type, type, (
% 49.99/32.70 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 49.99/32.70 tff(tptp_fun_W2_8_type, type, (
% 49.99/32.70 tptp_fun_W2_8: ( '$ki_world' * $i * $i ) > '$ki_world')).
% 49.99/32.70 tff(tptp_fun_B_25_type, type, (
% 49.99/32.70 tptp_fun_B_25: $i)).
% 49.99/32.70 tff(tptp_fun_W_24_type, type, (
% 49.99/32.70 tptp_fun_W_24: '$ki_world')).
% 49.99/32.70 tff(subset_type, type, (
% 49.99/32.70 subset: ( '$ki_world' * $i * $i ) > $o)).
% 49.99/32.70 tff(qmltpeq_type, type, (
% 49.99/32.70 qmltpeq: ( '$ki_world' * $i * $i ) > $o)).
% 49.99/32.70 tff(union_type, type, (
% 49.99/32.70 union: ( $i * $i ) > $i)).
% 49.99/32.70 tff(tptp_fun_W0_26_type, type, (
% 49.99/32.70 tptp_fun_W0_26: '$ki_world')).
% 49.99/32.70 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 49.99/32.70 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 49.99/32.70 tff(tptp_fun___ki_local_world__type, type, (
% 49.99/32.70 tptp_fun___ki_local_world_: '$ki_world')).
% 49.99/32.70 tff(1,assumption,(![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))), introduced(assumption)).
% 49.99/32.70 tff(2,plain,
% 49.99/32.70 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & (tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(3,plain,
% 49.99/32.70 (((~(~tptp_fun___ki_exists_in_world__i_(W!24, B!25))) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25)))) <=> (tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(4,plain,
% 49.99/32.70 ((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24))) <=> tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(5,plain,
% 49.99/32.70 (((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24))) & ((~(~tptp_fun___ki_exists_in_world__i_(W!24, B!25))) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & (tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25)))))),
% 49.99/32.70 inference(monotonicity,[status(thm)],[4, 3])).
% 49.99/32.70 tff(6,plain,
% 49.99/32.70 (((~(~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24))) & ((~(~tptp_fun___ki_exists_in_world__i_(W!24, B!25))) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))))),
% 49.99/32.70 inference(transitivity,[status(thm)],[5, 2])).
% 49.99/32.70 tff(7,plain,
% 49.99/32.70 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B)))))),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(8,plain,
% 49.99/32.70 ((~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, union(B, B), B))))) <=> (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B)))))),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(9,axiom,(~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => qmltpeq(W0, union(B, B), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 49.99/32.70 tff(10,plain,
% 49.99/32.70 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[9, 8])).
% 49.99/32.70 tff(11,plain,
% 49.99/32.70 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[10, 7])).
% 49.99/32.70 tff(12,plain,
% 49.99/32.70 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[11, 7])).
% 49.99/32.70 tff(13,plain,
% 49.99/32.70 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[12, 7])).
% 49.99/32.70 tff(14,plain,
% 49.99/32.70 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[13, 7])).
% 49.99/32.70 tff(15,plain,
% 49.99/32.70 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[14, 7])).
% 49.99/32.70 tff(16,plain,
% 49.99/32.70 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | qmltpeq(W0, union(B, B), B))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[15, 7])).
% 49.99/32.70 tff(17,plain,
% 49.99/32.70 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24) & tptp_fun___ki_exists_in_world__i_(W!24, B!25) & (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25)))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[16, 6])).
% 49.99/32.70 tff(18,plain,
% 49.99/32.70 (~((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))),
% 49.99/32.70 inference(and_elim,[status(thm)],[17])).
% 49.99/32.70 tff(19,plain,
% 49.99/32.70 (~qmltpeq(W0!26, union(B!25, B!25), B!25)),
% 49.99/32.70 inference(or_elim,[status(thm)],[18])).
% 49.99/32.70 tff(20,plain,
% 49.99/32.70 (tptp_fun___ki_accessible_(W!24, W0!26)),
% 49.99/32.70 inference(or_elim,[status(thm)],[18])).
% 49.99/32.70 tff(21,plain,
% 49.99/32.70 (((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(22,plain,
% 49.99/32.70 ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | ((~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25))),
% 49.99/32.70 inference(quant_inst,[status(thm)],[])).
% 49.99/32.70 tff(23,plain,
% 49.99/32.70 ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))) | (~tptp_fun___ki_accessible_(W!24, W0!26)) | qmltpeq(W0!26, union(B!25, B!25), B!25)),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[22, 21])).
% 49.99/32.70 tff(24,plain,
% 49.99/32.70 ($false),
% 49.99/32.70 inference(unit_resolution,[status(thm)],[23, 20, 19, 1])).
% 49.99/32.70 tff(25,plain,(~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))), inference(lemma,lemma(discharge,[]))).
% 49.99/32.70 tff(26,plain,
% 49.99/32.70 (^[W: '$ki_world'] : refl(tptp_fun___ki_accessible_(W, W) <=> tptp_fun___ki_accessible_(W, W))),
% 49.99/32.70 inference(bind,[status(th)],[])).
% 49.99/32.70 tff(27,plain,
% 49.99/32.70 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 49.99/32.70 inference(quant_intro,[status(thm)],[26])).
% 49.99/32.70 tff(28,plain,
% 49.99/32.70 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W) <=> ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(29,axiom,(![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive')).
% 49.99/32.70 tff(30,plain,
% 49.99/32.70 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[29, 28])).
% 49.99/32.70 tff(31,plain,(
% 49.99/32.70 ![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 49.99/32.70 inference(skolemize,[status(sab)],[30])).
% 49.99/32.70 tff(32,plain,
% 49.99/32.70 (![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[31, 27])).
% 49.99/32.70 tff(33,plain,
% 49.99/32.70 ((~![W: '$ki_world'] : tptp_fun___ki_accessible_(W, W)) | tptp_fun___ki_accessible_(W!24, W!24)),
% 49.99/32.70 inference(quant_inst,[status(thm)],[])).
% 49.99/32.70 tff(34,plain,
% 49.99/32.70 (tptp_fun___ki_accessible_(W!24, W!24)),
% 49.99/32.70 inference(unit_resolution,[status(thm)],[33, 32])).
% 49.99/32.70 tff(35,plain,
% 49.99/32.70 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)),
% 49.99/32.70 inference(and_elim,[status(thm)],[17])).
% 49.99/32.70 tff(36,plain,
% 49.99/32.70 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))))),
% 49.99/32.70 inference(bind,[status(th)],[])).
% 49.99/32.70 tff(37,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 49.99/32.70 inference(quant_intro,[status(thm)],[36])).
% 49.99/32.70 tff(38,plain,
% 49.99/32.70 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))))),
% 49.99/32.70 inference(bind,[status(th)],[])).
% 49.99/32.70 tff(39,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 49.99/32.70 inference(quant_intro,[status(thm)],[38])).
% 49.99/32.70 tff(40,plain,
% 49.99/32.70 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))))),
% 49.99/32.70 inference(bind,[status(th)],[])).
% 49.99/32.70 tff(41,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 49.99/32.70 inference(quant_intro,[status(thm)],[40])).
% 49.99/32.70 tff(42,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 49.99/32.70 inference(transitivity,[status(thm)],[41, 39])).
% 49.99/32.70 tff(43,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(44,plain,
% 49.99/32.70 (^[W: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: '$ki_world'] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W2: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))), (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) <=> ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))), quant_intro(proof_bind(^[W2: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)) <=> ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))), (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)) <=> ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))), ((![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))) <=> (![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) => ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))), rewrite((![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)) => ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))), ((![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))) <=> ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))) <=> (tptp_fun___ki_accessible_(W0, W1) => ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))), rewrite((tptp_fun___ki_accessible_(W0, W1) => ((~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))), ((tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))) <=> ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), (![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))) <=> ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))) <=> (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))), ((tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), (![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))) <=> ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))) <=> (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), rewrite((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))), ((tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))) <=> ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), (![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))) <=> ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))) <=> (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))) <=> ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))))),
% 49.99/32.70 inference(bind,[status(th)],[])).
% 49.99/32.70 tff(45,plain,
% 49.99/32.70 (![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C)))))))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 49.99/32.70 inference(quant_intro,[status(thm)],[44])).
% 49.99/32.70 tff(46,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => ![C: $i] : (tptp_fun___ki_exists_in_world__i_(W0, C) => ![W1: '$ki_world'] : (tptp_fun___ki_accessible_(W0, W1) => (![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => subset(W2, B, C)) => ![W2: '$ki_world'] : (tptp_fun___ki_accessible_(W1, W2) => qmltpeq(W2, union(B, C), C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_union')).
% 49.99/32.70 tff(47,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[46, 45])).
% 49.99/32.70 tff(48,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | subset(W2, B, C))))))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[47, 43])).
% 49.99/32.70 tff(49,plain,(
% 49.99/32.70 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 49.99/32.70 inference(skolemize,[status(sab)],[48])).
% 49.99/32.70 tff(50,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))))))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[49, 42])).
% 49.99/32.70 tff(51,plain,
% 49.99/32.70 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 49.99/32.70 inference(modus_ponens,[status(thm)],[50, 37])).
% 49.99/32.70 tff(52,plain,
% 49.99/32.70 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 49.99/32.70 inference(rewrite,[status(thm)],[])).
% 49.99/32.70 tff(53,plain,
% 49.99/32.70 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))),
% 50.06/32.70 inference(quant_inst,[status(thm)],[])).
% 50.06/32.70 tff(54,plain,
% 50.06/32.70 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C)))))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))),
% 50.06/32.70 inference(modus_ponens,[status(thm)],[53, 52])).
% 50.06/32.70 tff(55,plain,
% 50.06/32.70 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))),
% 50.06/32.70 inference(unit_resolution,[status(thm)],[54, 51, 35])).
% 50.06/32.70 tff(56,plain,
% 50.06/32.70 (tptp_fun___ki_exists_in_world__i_(W!24, B!25)),
% 50.06/32.70 inference(and_elim,[status(thm)],[17])).
% 50.06/32.70 tff(57,plain,
% 50.06/32.70 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))))),
% 50.06/32.70 inference(rewrite,[status(thm)],[])).
% 50.06/32.70 tff(58,plain,
% 50.06/32.70 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))))),
% 50.06/32.70 inference(quant_inst,[status(thm)],[])).
% 50.06/32.70 tff(59,plain,
% 50.06/32.70 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B))) | subset(tptp_fun_W2_8(W1, C, B), B, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B, C), C))))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 50.06/32.70 inference(modus_ponens,[status(thm)],[58, 57])).
% 50.06/32.70 tff(60,plain,
% 50.06/32.70 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 50.06/32.70 inference(unit_resolution,[status(thm)],[59, 56, 55])).
% 50.06/32.70 tff(61,plain,
% 50.06/32.70 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 50.06/32.70 inference(rewrite,[status(thm)],[])).
% 50.06/32.70 tff(62,plain,
% 50.06/32.70 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))),
% 50.06/32.71 inference(quant_inst,[status(thm)],[])).
% 50.06/32.71 tff(63,plain,
% 50.06/32.71 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W0, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W0, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C)))))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | ![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[62, 61])).
% 50.06/32.71 tff(64,plain,
% 50.06/32.71 (![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[63, 60, 34])).
% 50.06/32.71 tff(65,plain,
% 50.06/32.71 (((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))))) <=> ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))))),
% 50.06/32.71 inference(rewrite,[status(thm)],[])).
% 50.06/32.71 tff(66,plain,
% 50.06/32.71 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))))),
% 50.06/32.71 inference(quant_inst,[status(thm)],[])).
% 50.06/32.71 tff(67,plain,
% 50.06/32.71 ((~![C: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, C)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, C, B!25))) | subset(tptp_fun_W2_8(W1, C, B!25), B!25, C))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, C), C))))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[66, 65])).
% 50.06/32.71 tff(68,plain,
% 50.06/32.71 (![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[67, 56, 64])).
% 50.06/32.71 tff(69,plain,
% 50.06/32.71 (((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | (~((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) <=> ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | (~((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 50.06/32.71 inference(rewrite,[status(thm)],[])).
% 50.06/32.71 tff(70,plain,
% 50.06/32.71 ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | ((~tptp_fun___ki_accessible_(W!24, W!24)) | (~((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))),
% 50.06/32.71 inference(quant_inst,[status(thm)],[])).
% 50.06/32.71 tff(71,plain,
% 50.06/32.71 ((~![W1: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W1)) | (~((~tptp_fun___ki_accessible_(W1, tptp_fun_W2_8(W1, B!25, B!25))) | subset(tptp_fun_W2_8(W1, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W1, W2)) | qmltpeq(W2, union(B!25, B!25), B!25)))) | (~tptp_fun___ki_accessible_(W!24, W!24)) | (~((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[70, 69])).
% 50.06/32.71 tff(72,plain,
% 50.06/32.71 ((~((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))) | ![W2: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W2)) | qmltpeq(W2, union(B!25, B!25), B!25))),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[71, 34, 68])).
% 50.06/32.71 tff(73,plain,
% 50.06/32.71 (~((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[72, 25])).
% 50.06/32.71 tff(74,plain,
% 50.06/32.71 (((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25)) | tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))),
% 50.06/32.71 inference(tautology,[status(thm)],[])).
% 50.06/32.71 tff(75,plain,
% 50.06/32.71 (tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[74, 73])).
% 50.06/32.71 tff(76,plain,
% 50.06/32.71 (((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25)) | (~subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))),
% 50.06/32.71 inference(tautology,[status(thm)],[])).
% 50.06/32.71 tff(77,plain,
% 50.06/32.71 (~subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25)),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[76, 73])).
% 50.06/32.71 tff(78,assumption,(~subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25)), introduced(assumption)).
% 50.06/32.71 tff(79,assumption,(tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))), introduced(assumption)).
% 50.06/32.71 tff(80,plain,
% 50.06/32.71 (^[W: '$ki_world'] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))))),
% 50.06/32.71 inference(bind,[status(th)],[])).
% 50.06/32.71 tff(81,plain,
% 50.06/32.71 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(quant_intro,[status(thm)],[80])).
% 50.06/32.71 tff(82,plain,
% 50.06/32.71 (^[W: '$ki_world'] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))))),
% 50.06/32.71 inference(bind,[status(th)],[])).
% 50.06/32.71 tff(83,plain,
% 50.06/32.71 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(quant_intro,[status(thm)],[82])).
% 50.06/32.71 tff(84,plain,
% 50.06/32.71 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(transitivity,[status(thm)],[83, 81])).
% 50.06/32.71 tff(85,plain,
% 50.06/32.71 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(rewrite,[status(thm)],[])).
% 50.06/32.71 tff(86,plain,
% 50.06/32.71 (^[W: '$ki_world'] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[W0: '$ki_world'] : rewrite((tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B)) <=> ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))), (![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B)) <=> ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B))) <=> (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))), rewrite((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))), ((tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B))) <=> ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))))), (![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B))) <=> ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B)))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))))),
% 50.06/32.71 inference(bind,[status(th)],[])).
% 50.06/32.71 tff(87,plain,
% 50.06/32.71 (![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B)))) <=> ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(quant_intro,[status(thm)],[86])).
% 50.06/32.71 tff(88,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ![B: $i] : (tptp_fun___ki_exists_in_world__i_(W, B) => ![W0: '$ki_world'] : (tptp_fun___ki_accessible_(W, W0) => subset(W0, B, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_of_subset')).
% 50.06/32.71 tff(89,plain,
% 50.06/32.71 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[88, 87])).
% 50.06/32.71 tff(90,plain,
% 50.06/32.71 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[89, 85])).
% 50.06/32.71 tff(91,plain,(
% 50.06/32.71 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(skolemize,[status(sab)],[90])).
% 50.06/32.71 tff(92,plain,
% 50.06/32.71 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[91, 84])).
% 50.06/32.71 tff(93,plain,
% 50.06/32.71 (((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B))))) <=> ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(rewrite,[status(thm)],[])).
% 50.06/32.71 tff(94,plain,
% 50.06/32.71 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B))))),
% 50.06/32.71 inference(quant_inst,[status(thm)],[])).
% 50.06/32.71 tff(95,plain,
% 50.06/32.71 ((~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W, W0)) | subset(W0, B, B))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, W!24)) | ![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B)))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[94, 93])).
% 50.06/32.71 tff(96,plain,
% 50.06/32.71 (![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B)))),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[95, 92, 35])).
% 50.06/32.71 tff(97,plain,
% 50.06/32.71 (((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B)))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25)))) <=> ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B)))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25)))),
% 50.06/32.71 inference(rewrite,[status(thm)],[])).
% 50.06/32.71 tff(98,plain,
% 50.06/32.71 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B)))) | ((~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25)))),
% 50.06/32.71 inference(quant_inst,[status(thm)],[])).
% 50.06/32.71 tff(99,plain,
% 50.06/32.71 ((~![B: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!24, B)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B, B)))) | (~tptp_fun___ki_exists_in_world__i_(W!24, B!25)) | ![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25))),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[98, 97])).
% 50.06/32.71 tff(100,plain,
% 50.06/32.71 (![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25))),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[99, 56, 96])).
% 50.06/32.71 tff(101,plain,
% 50.06/32.71 (((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25))) | ((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))) <=> ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))),
% 50.06/32.71 inference(rewrite,[status(thm)],[])).
% 50.06/32.71 tff(102,plain,
% 50.06/32.71 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25))) | ((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25))),
% 50.06/32.71 inference(quant_inst,[status(thm)],[])).
% 50.06/32.71 tff(103,plain,
% 50.06/32.71 ((~![W0: '$ki_world'] : ((~tptp_fun___ki_accessible_(W!24, W0)) | subset(W0, B!25, B!25))) | (~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25)),
% 50.06/32.71 inference(modus_ponens,[status(thm)],[102, 101])).
% 50.06/32.71 tff(104,plain,
% 50.06/32.71 ($false),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[103, 100, 79, 78])).
% 50.06/32.71 tff(105,plain,((~tptp_fun___ki_accessible_(W!24, tptp_fun_W2_8(W!24, B!25, B!25))) | subset(tptp_fun_W2_8(W!24, B!25, B!25), B!25, B!25)), inference(lemma,lemma(discharge,[]))).
% 50.06/32.71 tff(106,plain,
% 50.06/32.71 ($false),
% 50.06/32.71 inference(unit_resolution,[status(thm)],[105, 77, 75])).
% 50.06/32.71 % SZS output end Proof
%------------------------------------------------------------------------------